High-contrast random systems of PDEs: homogenisation and spectral theory

Capoferri, Matteo, Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767 and Velčić, Igor 2025. High-contrast random systems of PDEs: homogenisation and spectral theory. Communications in Contemporary Mathematics 10.1142/S0219199725500294 Item availability restricted.

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Abstract

We develop a qualitative homogenization and spectral theory for elliptic systems of partial differential equations in divergence form with highly contrasting (i.e. non-uniformly elliptic) random coefficients. The focus of this paper is on the behavior of the spectrum as the heterogeneity parameter tends to zero; in particular, we show that in general one does not have Hausdorff convergence of spectra. The theoretical analysis is complemented by several explicit examples, showcasing the wider range of applications and physical effects of systems with random coefficients, when compared with systems with periodic coefficients or with scalar operators (both random and periodic).

Item Type:	Article
Date Type:	Published Online
Status:	In Press
Schools:	Schools > Mathematics
Publisher:	World Scientific Publishing
ISSN:	0219-1997
Date of First Compliant Deposit:	29 January 2025
Date of Acceptance:	19 January 2025
Last Modified:	24 Mar 2025 15:00
URI:	https://orca.cardiff.ac.uk/id/eprint/175699

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